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Simplifying F(x) = 2x2 + -8x Multiply F * x xF = 2x2 + -8x Reorder the terms: xF = -8x + 2x2 Solving xF = -8x + 2x2 Solving for variable 'x'. Reorder the terms: 8x + xF + -2x2 = -8x + 2x2 + 8x + -2x2 Reorder the terms: 8x + xF + -2x2 = -8x + 8x + 2x2 + -2x2 Combine like terms: -8x + 8x = 0 8x + xF + -2x2 = 0 + 2x2 + -2x2 8x + xF + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 8x + xF + -2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(8 + F + -2x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(8 + F + -2x)' equal to zero and attempt to solve: Simplifying 8 + F + -2x = 0 Solving 8 + F + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + F + -8 + -2x = 0 + -8 Reorder the terms: 8 + -8 + F + -2x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + F + -2x = 0 + -8 F + -2x = 0 + -8 Combine like terms: 0 + -8 = -8 F + -2x = -8 Add '-1F' to each side of the equation. F + -1F + -2x = -8 + -1F Combine like terms: F + -1F = 0 0 + -2x = -8 + -1F -2x = -8 + -1F Divide each side by '-2'. x = 4 + 0.5F Simplifying x = 4 + 0.5FSolution
x = {0, 4 + 0.5F}
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